Some signal transmitters for cellular communications utilize QAM (quadrature amplitude modulation) to increase the number of signals that can be transmitted on a given channel. QAM is a method of combining two amplitude-modulated (AM) signals into a single channel to effectively double the effective bandwidth. QAM is used with pulse amplitude modulation (PAM) in digital systems, especially in wireless applications.
In a QAM (quadrature amplitude modulation) signal, there are two carriers, each having the same frequency but differing in phase by 90 degrees (one quarter of a cycle, from which the term quadrature arises). The two modulated carriers are combined at the source for transmission. At the destination, the carriers are separated, the data is extracted from each, and then the data is combined into the original modulating information.
Radio transmitters amplify input signals. It is desired that the gain of such transmitters be linear for the entire range of input signals. Memoryless linearization of signal transmitters and, in particular, of radio transmitters is closely related to the problem of power amplifier linearization using baseband techniques, which is considered to be of the greatest significance for achieving effective and economical minimization of transmission-related signal distortions in digital communication systems. Despite a big diversity of existing approaches aimed at improving the quality of RF power amplification, many of the older solutions are constrained to usage with specific discrete-level signaling formats, and, thus have a limited relevance to contemporary wideband communication standards. Development of general solutions of a particular practical value that are invariant with respect to the transmitted signal has been simulated in the past decade, pointing out the usefulness of a single-argument complex gain function of the input power for the modeling of memoryless distortions in baseband power amplifier linearizers. Compared to the previously demonstrated general approach using two-dimensional mapping of the amplifier output against the phase and magnitude signal values at its input, the gain-based nonlinear model has a substantially lower computational complexity for the same performance that is instrumental in the design of hardware-efficient digital linearization systems.
A common architecture of recently proposed baseband power amplifier linearizers includes a digital nonlinear gain block, usually called a predistortion block, inserted in the transmitter chain prior to upconversion stages. It is continuously adapted to approximate as closely as possible the inverse nonlinear complex gain of the following transmitter stages up to the power amplifier. Depending on the coordinate system in which the transmitter gain estimation is conducted two main types of baseband linearization approaches can be distinguished: (1) orthogonal-coordinate, where the complex gain function is defined by a pair of real and imaginary functions, and (2) polar-coordinate, where the complex gain function is defined by a magnitude and a phase function. Since in QAM schemes the signals are typically represented by in-phase and quadrature-phase components, i.e. in orthogonal coordinates, the realization of the second approach involves additional complexity to provide for coordinate system transformation of the estimation data. On the other hand, more sophisticated adaptation algorithms are required for the implementation of unconditionally convergent and robust baseband linearization in orthogonal coordinates.
For QAM signaling schemes, such as CDMA and UMTS, the realization of the first approach would be naturally simpler since signal format conversions could be avoided. On the other hand, from the perspective of real-time adaptation of the predistorter gain more complexity should be added to the respective algorithms because of the nonlinear behavior of the predistortion gain gradient as a function of the average phase of the linearized transmitter gain.
The realization of the second linearization approach requires additional means for coordinate system transformation of the estimation data and the predistorted signal such as orthogonal-to-polar and polar-to-orthogonal conversion blocks (note that this is true if the signal is represented by its in-phase/quadrature-phase components in the transmitter). The major advantage of using polar-coordinate representation of the linearized transmitter gain is that the iterative derivation of the predistortion gain is invariant with respect to the average gain phase in this coordinate system. On the other hand, the biggest disadvantages are the large amount of hardware resources needed for the implementation of precision trigonometric/inverse-trigonometric functions performing the coordinate transformations and, most importantly, the noise-biasing effects associated with processing the modulus of noisy complex data.
Although offering a basis for potentially more efficient implementation of predistorter adaptation algorithms, the orthogonal coordinate approach has been a subject of analyses and evolution in only few theoretical and experimental studies. The two existing forms of orthogonal adaptation can be viewed as first and second order approximations of Newton's method for numerical minimization of functions with complex variable using consecutive iterations proportional to the function first derivative. The first and less accurate approximation uses a single constant to represent the average absolute value of the first derivative (a linear iteration method); while the second and more accurate one uses the ratio of finite function and argument differences for continuous first derivative estimation (a secant iteration method). The first adaptation approach totally ignores the phase of the function argument and by this introduces ambiguity with respect to it, which practically makes the algorithm convergence dependent on the signal phase rotation taking place in the transmitter. This limitation can be overcome by an additional signal phase rotation in the algorithm to equalize for it. The second adaptation approach does not have this disadvantage and provides faster convergence towards the function minimum but involves a division operation that increases its susceptibility to noise.
In one attempt to provide a linearized system, a rectangular representation of the data is used in error processing circuits along with a proportional-integral adaptation algorithm. However, the error formation circuits involve a highly inefficient complex division operation. Moreover, an additional rotation of the phase of the feedback signal derived from the transmitter output is required for stable algorithm operation.
Same data representation has been recently adopted in a method of linearizing a power amplifier in a mobile communication system, where the division operation is avoided while using simple integration of the scaled error signal under the assumption that the average phase difference between the input signal to the transmitter and the feedback signal is small. Nevertheless, the overall system complexity remains high since correction of the transmitted signal phase is performed using a delay line prior to power amplification. In addition, the fixed amount of phase correction typically provided by the delay line should match the average phase rotation caused by the analog system components and, thus, may not always be convenient in practical cases.
In yet another approach, amplifier linearization by adaptive predistortion is attempted. The linearization algorithm is stable with respect to the phase of the feedback signal since it uses a secant iteration method involving the phase of the error as a separate term to perform faster adaptation of the predistortion gain. Nevertheless, this algorithm still requires a complex division by the error signal, which is not only inefficient but also increases the system susceptibility to noise.
An unconditionally stable baseband linearization method performs adaptation in polar coordinates, while representing the predistortion gain by its magnitude and phase components. Although realized by a fairly simple and robust adaptive algorithm, such methods have substantial implementation complexity because of the use of orthogonal-to-polar-to-orthogonal coordinate conversion of the input signal as well as orthogonal-to-polar transformation of the feedback signal. Moreover, the estimation of the predistortion gain magnitude is biased proportionally to the noise power in the feedback channel.
A linearization system utilizes polar-coordinate signal representation of data in the adaptive predistortion algorithm, which is invariant with respect to the average phase of the transmitter gain. First, the transmitter gain is estimated by applying forward system modeling, and, afterwards it is inverted into predistortion magnitude and phase. The inversion is implemented using polar-coordinate representation and avoids complex division operations required in the orthogonal-coordinate number format. The method involves inefficient coordinate system transformations of the input and feedback signals as well as extra means to implement (real-time) inversion of an arbitrary real-valued function. In addition, the predistortion gain is realized in two steps using a scaling operation and a multiplication by complex exponent function operation.